(I'm certain that the following would be rejected out of hand by almost everybody, but it is eminently fair.) I propose fractional electoral votes. If a state has, say, exactly 5.1% of the population, they would get 5.1% times 438 plus 2, or 24.338 electoral votes. Furthermore, for the purposes of tallying votes in the House, each of the 22 representatives would receive 1.01037 votes. (Note: If a state has 5.1% of the US population, it will have about 5.11% of the population EXCLUDING D.C. That's why 1.01037 times 22 plus 2 is a bit less than the number of electoral votes that I would assign to this state.)

9:29 am April 25, 2008

Ernest J Moosa Jr wrote:

The answer should be rather straightforward. Increase the number of representatives so that we have the same number of citizens per district as we had (pick a year-I'll say 1910). As the population continues to grow, the resulting loss of a representative by fractions to any particular state will diminish substantially. And we get back towards a more real sense of representation in this country. Add to that the chance to have many new seats without incumbents defending those seats, and the political reality in this nation changes dramatically.

9:36 am April 25, 2008

Adam Shane wrote:

Very interesting article. Thank you.

First of all, the arbitrary 435-seat limit in the House needs to be removed. Prior to 1920 (I believe) the number of seats grew as the US pop. grew. The number of seats was roughly equal to the cube root of the pop., which is considered by some to be a good rule of thumb. According to the 2000 census, the US pop. was 281,421,906, the cube root of which is 655. I would increase the size of the House to 655 and apportion seats per Hamilton's method. It seems to make sense that a state with a higher fractional percentage of the population should get priority in receiving the "incremental" seats.

9:37 am April 25, 2008

Bud Norton wrote:

I'm not a statistician, but I wonder how the following approach would stack up for fairness: start with a presumption of a House of 435 members, assign each state its share based on population, then round up or down to the nearest whole number. You'd probably never wind up with a House of exactly 435, but it would be close (I assume the odds are very much against the eventual total approaching the extremes of 385 and 485), and there's no inherent significance or symbolism to the number 435. I can see two objections (I'm sure there are more): 1. you might lose the odd number total (but surely the House has had an even number of voting representatives many times due to absences or vacancies). 2. for Electoral College purposes the 100 extra votes for the Senate loom larger or smaller depending on the size of the House. How much, though, and how significantly/ unfairly? And could #2 be solved by the fractional electoral votes proposed by Mr. Levene?

9:40 am April 25, 2008

John Davidson wrote:

A fascinating article, if a bit above my level in statistics.

Overseas Americans have asked for years to be counted in the decennial census, to no avail so far although Rep. Carolyn Maloney (D-NY) has championed the cause more recently, or actually since even before the 2000 census. Problem is, the Congress (and the framers of the constitution) actually wants to count the number of (live) bodies in their district. This goes back to Article 1 of the constitution and the famous "3/5 compromise". Enhancements to democracy (e.g. giving overseas U.S. citizens the right to vote in federal elections) have indeed spurred members of Congress to think — very occasionally — about their constituents who, by definition, vote in their district but don't live there.

You could also consider how counting Americans overseas in 2010 would affect state representation in the House. If there are six million Americans overseas, and a quarter of them vote in NY state (1/4 of the members of the Assoc of Americans Resident Overseas who indicate the state where they vote say it's NY), that would add 1.5 million to NY state's population, equivalent to two seats in the House. Well, by golly, in the redistricting after the 2000 census, guess how many House seats NY lost! Right: two.

10:31 am April 25, 2008

John King wrote:

It is up to each state whether to adopt a winner-take-all or some other method of allocating electoral votes, such as one electoral vote for each district a candidate carries plus the extra two for the candidate who wins the most districts or the popular vote. (The latter is necessary if there are two candidates and the state has an even number of congressional districts.) Only two state, Maine and Nebraska, have opted for one congressional district, one electoral vote.

This method does not solve the "rounding off" problem, but it does have the benefit of giving each district some say in the outcome. For example, President Bush easily won Texas in the last election but lost in Houston. In the per district method, no candidate could take any state for granted. Because of this, a state that feels shortchanged in the rounding off will nonetheless not be subject in the same way to the weight of a big state unless one candidate carries all of the districts, which is unlikely.

There is already a bias in the system that no amount of rounding off will solve: The extra two votes for each state (representing the number of senators). Before the 17th amendment, state legislators picked the senators (think Lincoln and Douglas), now the people do (which has had the effect of making the senate a group of 100 six year congressmen). The current senate therefore represents the people of each state and is not accountable to the state as a whole, the initial justification for adding the two electoral votes.

A small state with 2% of the population of a larger share may nonetheless have 10% of the electoral votes that that larger state has. Even if we could solve the rounding off problem, small states will still have more weight in the electoral college than their populations can justify.

Of course, those small states would never have joined the union were it not for the 2 extra electoral votes for their state, as a state. And three quarters of the states will never agree to change it because the smaller states would have to agree, and they obviously would not.

11:12 am April 25, 2008

Paul Morabito wrote:

I am curious as to why everyone focuses on number of states won and popular vote, rather than looking at Electoral College comparisons. The Democratic race is based on proportionate allocation of delegates by voting, but the Presidential race (and most GOP primaries) are winner take all. What happens when you take the Electoral Votes of the states Clinton has won vs that of Obama ? Who wins then ?

If you take the states that Clinton has won vs Obama, and compare total Electoral College votes, she wins 284 to 197. If you then take only those states won by Al Gore in 2000, she still wins 160 to 93.

If one thing that 2000 should have taught Democrats is that you need to win in the Electoral College. Not the popular votes. We are a collection of fifty State elections, not a national popularity contest.

I plan on backing John McCain. Frankly, I think Obama is the weakest general election candidate for the Democrats. Americans elect a President based on a assessing their character, experience and proposals.

I refuse to believe that a candidate whose parents met taking Russian language classes in Hawaii at the height of the Cuban missile crisis; who has never visited Europe but spent his gap year touring Pakistan in the late eighties; who looks at small town Americans, and their values, as "bitter" when they back the Second Amendment or celebrate their faith. I think Obama is a talented intellectual - I do not believe he will be able to connect with the American people in a general election fight with the Republicans.

I feel much more comfortable with a Commander in Chief who gave up five and a half years of his life in defense of liberty. I think a President like that would never permit torture; would reign back the Patriot Act to protect our freedom; would make tax cuts only after cutting spending; and would recognize that the ultimate responsibility that he has is to protect and defend the Constitution of the United States.

Clinton is a lot closer to 270 Electoral College votes needed to win than Obama is - plain and simple.

11:43 am April 25, 2008

Ed Nelson wrote:

I come from a small state (Mississippi) but to me the answer to the House question is a matter of fairness. Small states already have absolutely equal power in the Senate with large states; the large states should then be awarded the fractional House representatives, starting from the largest state down (i.e. California would always get a fractional, Texas, New York, etc). Once you reach 435, you are done.

12:36 pm April 25, 2008

Anonymous wrote:

I am still as shocked now as when I first learned back in elementary school that we do not vote directly for the President of the United States. The electorial college should be eliminated and we should have a straight popular vote just like any other elected office.

1:59 pm April 25, 2008

Peter Foley wrote:

What about the far larger problem of counting all persons that now includes illegal and legal aliens to determine apportionment? We need to amend the 14th Amendment to end enumeration of aliens.

3:05 pm April 25, 2008

F wrote:

I also think we need more representatives. When each Congressman represents nearly a million people, that's not really representation. Somewhere about double sounds right to me, but the cube root rule would be okay too.

3:49 pm April 25, 2008

Pat Thompson wrote:

With telecommunications being what it is today there is no reason that the US couldn't institute a true representative House.

Simply stated, use the population of the smallest state as X (thus setting the value per representative) and divide X into each state's population to determine the number of representatives. Using 2000 Census, Wyoming with 494K sets X and total population at 281M, that would mean a total of 569 representatives.

Now, to reduce the burden in DC, use one of the methods described above to set the number who would be in DC at any one time. For those not in DC, they would still be able to debate (via teleconferencing) and vote (secured network) on all the bills and laws.

Now, in order to insure each representative has direct contact in DC during their term, each state that has more representatives than seat allocations in DC could divide their representatives in halves with the first half being in DC for the 1st year followed by the 2nd half being their the 2nd year (or it could be split into half year increments, I suppose?)

This would be readjusted after every census, as done now.

This would get back to the true representative democracy envisioned way back when but not possible due to technological limitations that no longer exist.

4:01 pm April 25, 2008

Edward Mandel House wrote:

These recurring articles are an indication that the powers that be are attempting to destroy the electoral college and our representative republic. If these articles continue and they are successful and unauditable electronic voting machines which are then counted by private companies with no paper trail backup go unquestioned, the powers that be will be successful and the American experiment will be a failed footnote in history. We will then revert back to a feudal system of serfdom. We will return to what famed Jesuit James Walsh called the "Greatest of Centuries"--the Thirteenth century and we will all be serfs again. Wake up everybody before it's too late.

4:40 pm April 25, 2008

Edward W. N. Smith wrote:

Your April 25, 2008 article “Bad Math = Mad Politics” identified some very interesting dynamics. As an employee compensation professional (dealing with similar dynamics affecting employees’ wallets…) I have had the chance to wrestle with many of the same issues.

I agree with the comment by David A. Levine that can be summarized as “Don’t round.” (The US Constitution not withstanding…) I can see no reason why, for instance, my home state of Pennsylvania shouldn’t get 23.475 votes in the Electoral College (2 Senate seats + 21.475 – un-rounded – House of Representative seats).

If Wendy’s shareholders can get fractional (4.25) shares of Triarc stock for each share of Wendy’s they own (WSJ, April 25, 2008, B1, “After Two Years, Peltz Finally Makes a Deal for Wendy’s”), why not have fractional voting in the Electoral College? For convenience sake we may wish to round, to, say, 3 decimal points, but, that is something else that can be negotiated in a Conference Committee.

Another advantage: Reduced likelihood of a tie…

5:19 pm April 25, 2008

Joseph N. wrote:

When I studied this all those years ago in college (interestingly , it was in political science, not statistics) I saw the problem was the limit of 435. What a pleasure to come here today and see other people see the same problem.

Let's be honest about what is the complaint: the fight is over the LAST seat in the House, the last piece of pie.

The districts have grown large enough to be easily pulled an stretched into gerrymandered districts. the reps. don't represent the people. They are tools of the two parties.

Smaller districts, combined with a get tough attitude by court against gerrymandering, would make the House more representative, as well as make the "last seat" less valuable.

I found the flash presentation very interesting. The MTD method does solve the political problem, but mathematically, it clearly steals from the rich (big states) to give to the poor.

A tidbit that goes unmentioned is that the govt. does not divide all 435 seats. Since each state must get at least one, those are handed out first, and the "divisor" math is only performed on the remaining seats.

6:18 pm April 25, 2008

Prof. John Banzhaf, GWU University wrote:

A LONG LETTER ON A CLOSELY RELATED TOPIC

I write to suggest a follow up article entitled “The Electoral College’s Subtle Math II” which would explore two additional related issues concerned with the mathematics of the Electoral College.

FIRST, politicians and commentators – many of whom should know better – believe and write that voters in the least populous states have more voting power than voters in other states. For example, the Washington Lawyer recently stated that residents of less populous states have greater voting power than others "because every state is given a two-vote bonus, the small states have fewer people per elector and therefore more of a say." “Electoral College Reform” [10/07]. This belief, it seems, creates resistance to any kind of reform – including a constitutional amendment providing for the direct election of the president, or a new movement which seeks to accomplish much the same without the need for a constitutional amendment [www.nationalpopularvote.com].

However, detailed calculations I made shortly after leaving law school – and based upon the “Banzhaf Index of Voting Power” which I developed while in law school as a reaction to one of my law professors – clearly show that the effect of “fewer people per elector” in less populous states is totally overwhelmed by the much greater ability of voters in populous states to affect how the state’s large bloc of electoral votes will be cast [under the winner-take-all system] [see Banzhaf, 3.312 Votes, A Mathematical Analysis of the Electoral College, 13 Villanova L. Rev. 303 (1968); see generally http://www.cs.unc.edu/~livingst/Banzhaf/

As you may know, my calculations provided some of the basis for an almost-successful attempt to abolish the Electoral College [Election of the President, Hearings before the Subcommittee on Constitutional Amendments, U.S. Senate, p. 517-42, 904-33; Electoral College Reform, Hearings before the Committee on the Judiciary, House of Representatives, p. 306-74]; were widely adopted by books on the topic [see, e.g., Michener, Presidential Lottery, Part C entitled "The Banzhaf Studies" at 220 (1969); Pierce, The People's President, Section O entitled "Computer Analysis of Large versus Small State Power in the Electoral College" at 362 (1968)]; and were even reported in the popular press [see, e.g., Editorial, St. Louis Post-Dispatch, Nov. 24, 1968; Editorial, The New York Times, Dec. 18, 1968; Editorial, The Washington Post, Dec. 31, 1967; The Games Scholars Play, Newsweek, Sept. 6, 1982 (on game theory)].

In summary, while the number of each state’s electoral votes is roughly proportional to its population, the ability of a citizen to cast a decisive vote is inversely proportional not to the population but rather to the square root of the population. This explains why a citizen in California has almost 3.5 times the chance of casting a deciding vote for president as a citizen of Montana, even though Montanans have twice the [fractional] number of electoral voters per voter as Californians [http://banzhaf.net/ec2000.html].

I think an article describing and discussing this widely held myth concerning the Electoral College, a myth one which may well impede efforts towards change, would be welcome and interesting. It would also raise the broader issue of how one truly determines and compares voting power in other complex voting situations, including:

A. Weighted voting [see Banzhaf, Weighted Voting Doesn't Work: A Mathematical Analysis, 19 Rutgers L. Rev. 317 (1965), which became the law of New York State in the judicial opinion: Iannucci v. Board of Supervisors, 229 N.E. 2d 195 (1967)]

SECOND, I think it would be very interesting to see how this discussion could be combined with an analysis of how the major candidates for president might use mathematics to help determine the most effective way to allocate scarce campaign resources (e.g., money, candidate’s time, etc.) among various states so as to have the greatest chance of improving their odds to win the election for the lowest cost.

While it has been reported that “presidential candidates concentrate over two-thirds of their advertising money and campaign visits in just six states, and over 99% of their advertising money in just 16 states,” the precise methods or algorisms for picking these states has rarely if ever been discussed, and may well be based more on hunch and feel that on any more precise analysis. However, such an analysis would probably be based upon how close the voters appear to be in particular states (and how many undecided voters there are), what it might take (e.g., a change in position, a campaign stop) to persuade voters in a particular state to change their votes, the cost of reaching voters in each state (e.g., in terms of television time, etc.), as well as their theoretical voting power in terms of their relative chances of affecting the outcome of the election with their votes.

These are my preliminary ideas. Needless to say, I would be delighted to discuss these topics further with you.

9:33 pm April 25, 2008

chip greenblatt wrote:

It is indeed provable the no method will preserve quota and avoid the Alabama Paradox for every h and every census. The proof involves the fact that the remainder is modulo 1 arithmetic and is not monotonic for each state wrt h for some sets of values. On the other hand it is provable that there always exists a new h more than one larger such that the paradox never happens with the increase to the new h.
Lastly this argument about the electoral college is extremely tiresome as there exists no procedure which will always select the most preferred candidate if there are more than two candidates on the ballot at any point in selection. Further why would the third plus one smaller States ever accept a diminution of their political power by giving up their two point bias which is most of their electoral power? I am willing to bet any amount that this won't happen in any reasonably finite time.

8:34 am April 26, 2008

Nikki wrote:

For the 1876 election - it was not bad math at all...it was out and out fraud and theft. 3 states submitted 2 and 3 sets of Electoral College votes for Congress to count...each side - Dem and Rep submitted...the Republicans were cheating to win. This particular election is where all election theft began.

5:43 pm April 26, 2008

Tort Reform wrote:

Nice article, but it misses the point. We need to privatize our government and let business run America. The United States Chamber of Commerce could be like our new House of Representatives. That way we could leave behind all this mess y and inefficient politicking and just stick to making money.

9:45 pm April 27, 2008

Chuck Sonnenschein wrote:

I thoroughly enjoyed your article in the WSJ, and, although I read it several times, I still have two questions.
1. I do not understand how you can can get the Alabama paradox using the Hamilton’s procedure described in the article. I will describe the procedure as I understand it. First calculate the quotas of all of the states; then sum them. (The sum must be a whole number equal to the number of House seats.) Next round down all of the quotas and sum these numbers. (This sum must also be a whole number less than or equal to the number of House seats.) Take the difference between these two sums, which also must be a whole number; call this value the SumDifference. Now award each state a number of House seats equal to its rounded down quota. (The number or awarded House seats will be equal to Next take the differences between the state quotas and the state rounded-down numbers. Arrange the states in a monotonically decreasing order depending on these differences. Divide the state list into two parts: the first part contains the state at the beginning of the monotonically decreasing list and continues down the list until the number of members in the first part is equal to the value of the SumDifference; the other part of the list contains all other states. Award each of the states in the first part of the list an additional seat. This should award all of the House seats, and I do not see how this method can cause any state to lose a House seat.
2. Please describe the Webster method.

11:27 pm April 27, 2008

Alan wrote:

Dumb question, but why not just adjust the number of representatives after each census? Didn't Congress temporarily expand to 437 representatives after Alaska and Hawaii were admitted to the Union? If we say that each representative should represent roughly 690,000 (300 million / 435), why not just add or subtract a few from that to ensure that there are no "fractions", setting .5 as a "hard" rounding point? It still leads to a few anomalies, but is better than court fights and gamesmanship, right? With 500 representatives as the "target" (600,000 per representative) there are even fewer anomalies

9:40 am April 28, 2008

Clinton wrote:

Short of going with popular vote, I don't think there is a particularly foolproof improvement to the electoral college as it exists today. Any of the discussed permutations still has the ability to amplify small differences in popular votes when those differences exist in specific regions.

11:33 am April 28, 2008

Bob Jones wrote:

How about this...go to a popular vote. No one can argue that isn't fair, and no argument of what formula to use. That is as straight forward as it gets. Why should a person in North Dakota have less of a say in the election than someone in Califonia? That's what the electoral college system does. And you can't blame me for being biased, because I actually live in New York, one of the most populous states.

Editor Comment

2:50 pm April 28, 2008

Carl Bialik wrote:

In reply to Chuck:

1 -- The paradox has arisen when Congress considered increasing its overall size. When that happens, no single state should lose seats, but it can happen with Hamilton, because of differences in rounding. It's explained in the Congressional Research Service report linked from "further reading."

2 -- Click on the image at top of the post that says See more electoral math, history for details on all the methods.

2:45 pm April 30, 2008

freelunch wrote:

Why should a person in North Dakota have less of a say in the election than someone in Califonia? That’s what the electoral college system does.
.
No, each voter in ND has more power than in CA. The bloc voting of the EC does offset some of the problem, but it is possible for someone to win the presidency by winning only small states that contain less than half of the population of the country. If you win only large states, you must have more than half of the population of the country to win.

10:22 am September 12, 2008

john peter wrote:

Have studied this for hours upon hours every national election year and still haven't a clue as to how it it has survived. It is simply tiring explaining it and studying it- almost as tiring as this country's bogus "two party system" that we are forced to participate in IF we choose to vote. Bottom line is, if 200 million people vote, then 200 million votes should be properly counted and the winner named the winner based on popular vote. PERIOD. It is beyond me that A) This archaic system is still in place in 2008 when every tiny corner of this country is more connected via internet and cable television than ever, and B) WHY THE PUNDITS ON TV OR RADIO NEVER TALKS ABOUT IT!!!! EVER! Most importantly, if everyone knew clearly that their vote TRULY counted in whatever state they lived in and that their vote could not be over ridden because they live in a "blue or a red state" then more people would vote. Absolutely assinine.

9:06 pm October 4, 2008

S. Frantz wrote:

Having wondered for years about the fairness of the Electoral College, let this country do something easy once. Do away with the Electoral College and give the position to the winner in the popular vote. At least the voters would feel as if they had elected their own president. It is time for change in this country. This is the twenty first century and we are still using an archaic system Thank you.

method

7:50 pm October 24, 2008

Jeremy Goodell wrote:

’m so tired of the Electoral College and the two party system. Once this election is over, I intend to devote a lot of my time and energy to efforts to abolish both. When did the U.S. become a bunch of red and blue states? How come my vote (as a Californian) hasn’t counted in 30 years? Nobody campaigns in California, New York, Texas, Illinois … those states are already decided. Why is it that the most important voters are in Ohio, Florida, New Mexico and Indiana? Seems a bit backwards, doesn’t it?

See my “Know More” blog at http://www.jeremygoodell.com. The other day I posted an entry about the Electoral College that points out a bit of a loophole that could be exploited to win an election.

2:59 pm October 29, 2008

Patricia wrote:

I am interested in the names of the electoral candidates are in New York. How can they be found?

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About The Numbers

The Wall Street Journal examines numbers in the news, business and politics. Some numbers are flat-out wrong or biased, while others are valid and help us make informed decisions. We tell the stories behind the stats in occasional updates on this blog.